Rewrite as a simplified fraction. ${3.71\overline{2} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3712.2222...\\ 100x &= 371.2222...\end{align*}}$ Subtracting the two equations, we have: ${900x = 3341}$ ${x = \dfrac{3341}{900}} \text{or} {3 \dfrac{641}{900}}$